arcgis.geometry.functions module¶
Functions which take geometric types as parameters and return geometric type results.
areas_and_lengths¶

arcgis.geometry.functions.
areas_and_lengths
(polygons, length_unit, area_unit, calculation_type, spatial_ref=4326, gis=None)¶ The areas_and_lengths function calculates areas and perimeter lengths for each polygon specified in the input array.
 Inputs:
 polygons  The array of polygons whose areas and lengths are
to be computed.
 length_unit  The length unit in which the perimeters of
polygons will be calculated. If calculation_type is planar, then length_unit can be any esriUnits constant. If lengthUnit is not specified, the units are derived from spatial_ref. If calculationType is not planar, then lengthUnit must be a linear esriUnits constant, such as esriSRUnit_Meter or esriSRUnit_SurveyMile. If length_unit is not specified, the units are meters. For a list of valid units, see esriSRUnitType Constants and esriSRUnit2Type Constant.
 area_unit  The area unit in which areas of polygons will be
calculated. If calculation_type is planar, then area_unit can be any esriUnits constant. If area_unit is not specified, the units are derived from spatial_ref. If calculation_type is not planar, then area_unit must be a linear esriUnits constant such as esriSRUnit_Meter or esriSRUnit_SurveyMile. If area_unit is not specified, then the units are meters. For a list of valid units, see esriSRUnitType Constants and esriSRUnit2Type constant. The list of valid esriAreaUnits constants include, esriSquareInches  esriSquareFeet  esriSquareYards  esriAcres  esriSquareMiles  esriSquareMillimeters  esriSquareCentimeters  esriSquareDecimeters  esriSquareMeters  esriAres  esriHectares  esriSquareKilometers.
 calculation_type  The type defined for the area and length
calculation of the input geometries. The type can be one of the following values: planar  Planar measurements use 2D
Euclidean distance to calculate area and length. Th should only be used if the area or length needs to be calculated in the given spatial reference. Otherwise, use preserveShape.
 geodesic  Use this type if you want to
calculate an area or length using only the vertices of the polygon and define the lines between the points as geodesic segments independent of the actual shape of the polygon. A geodesic segment is the shortest path between two points on an ellipsoid.
 preserveShape  This type calculates the
area or length of the geometry on the surface of the Earth ellipsoid. The shape of the geometry in its coordinate system is preserved.
 Output:
JSON as dictionary
auto_complete¶

arcgis.geometry.functions.
auto_complete
(polygons=None, polylines=None, spatial_ref=None, gis=None)¶ The auto_complete function simplifies the process of constructing new polygons that are adjacent to other polygons. It constructs polygons that fill in the gaps between existing polygons and a set of polylines.
 Inputs:
 polygons 
array of Polygon objects
 polylines 
list of Polyline objects
 spatial_ref 
spatial reference of the input geometries WKID
buffer¶

arcgis.geometry.functions.
buffer
(geometries, in_sr, distances, unit, out_sr=None, buffer_sr=None, union_results=None, geodesic=None, gis=None)¶ The buffer function is performed on a geometry service resource The result of this function is buffered polygons at the specified distances for the input geometry array. Options are available to union buffers and to use geodesic distance.
Inputs:
 geometries 
The array of geometries to be buffered.
 in_sr 
The wellknown ID of the spatial reference or a spatial reference JSON object for the input geometries.
 distances 
The distances that each of the input geometries is buffered.
 unit  The units for calculating each buffer distance. If unit
is not specified, the units are derived from bufferSR. If bufferSR is not specified, the units are derived from in_sr.
 out_sr  The wellknown ID of the spatial reference or a
spatial reference JSON object for the input geometries.
 buffer_sr  The wellknown ID of the spatial reference or a
spatial reference JSON object for the input geometries.
 union_results  If true, all geometries buffered at a given
distance are unioned into a single (gis,possibly multipart) polygon, and the unioned geometry is placed in the output array. The default is false
 geodesic  Set geodesic to true to buffer the input geometries
using geodesic distance. Geodesic distance is the shortest path between two points along the ellipsoid of the earth. If geodesic is set to false, the 2D Euclidean distance is used to buffer the input geometries. The default value depends on the geometry type, unit and bufferSR.
convex_hull¶

arcgis.geometry.functions.
convex_hull
(geometries, spatial_ref=None, gis=None)¶ The convex_hull function is performed on a geometry service resource. It returns the convex hull of the input geometry. The input geometry can be a point, multipoint, polyline, or polygon. The convex hull is typically a polygon but can also be a polyline or point in degenerate cases.
 Inputs:
geometries  The geometries whose convex hull is to be created. spatial_ref  The wellknown ID or a spatial reference JSON object for
the output geometry.
cut¶

arcgis.geometry.functions.
cut
(cutter, target, spatial_ref=None, gis=None)¶ The cut function is performed on a geometry service resource. This function splits the target polyline or polygon where it’s crossed by the cutter polyline. At 10.1 and later, this function calls simplify on the input cutter and target geometries.
 Inputs:
 cutter  The polyline that will be used to divide the target
into pieces where it crosses the target.The spatial reference of the polylines is specified by spatial_ref. The structure of the polyline is the same as the structure of the JSON polyline objects returned by the ArcGIS REST API.
 target  The array of polylines/polygons to be cut. The
structure of the geometry is the same as the structure of the JSON geometry objects returned by the ArcGIS REST API. The spatial reference of the target geometry array is specified by spatial_ref.
 spatial_ref  The wellknown ID or a spatial reference JSON object for
the output geometry.
densify¶

arcgis.geometry.functions.
densify
(geometries, spatial_ref, max_segment_length, length_unit, geodesic=False, gis=None)¶ The densify function is performed using the GIS’s geometry engine. This function densifies geometries by plotting points between existing vertices.
 Inputs:
 geometries  The array of geometries to be densified. The
structure of each geometry in the array is the same as the structure of the JSON geometry objects returned by the ArcGIS REST API.
 spatial_ref  The wellknown ID or a spatial reference JSON object for
the input polylines. For a list of valid WKID values, see Projected coordinate systems and Geographic coordinate systems.
 max_segment_length  All segments longer than maxSegmentLength are
replaced with sequences of lines no longer than max_segment_length.
 length_unit  The length unit of max_segment_length. If geodesic is
set to false, then the units are derived from spatial_ref, and length_unit is ignored. If geodesic is set to true, then length_unit must be a linear unit. In a case where length_unit is not specified and spatial_ref is a PCS, the units are derived from spatial_ref. In a case where length_unit is not specified and spatial_ref is a GCS, then the units are meters.
 geodesic  If geodesic is set to true, then geodesic distance is
used to calculate max_segment_length. Geodesic distance is the shortest path between two points along the ellipsoid of the earth. If geodesic is set to false, then 2D Euclidean distance is used to calculate max_segment_length. The default is false.
difference¶

arcgis.geometry.functions.
difference
(geometries, spatial_ref, geometry, gis=None)¶ The difference function is performed on a geometry service resource. This function constructs the settheoretic difference between each element of an array of geometries and another geometry the socalled difference geometry. In other words, let B be the difference geometry. For each geometry, A, in the input geometry array, it constructs AB.
 Inputs:
 geometries  An array of points, multipoints, polylines or
polygons. The structure of each geometry in the array is the same as the structure of the JSON geometry objects returned by the ArcGIS REST API.
 geometry  A single geometry of any type and of a dimension equal
to or greater than the elements of geometries. The structure of geometry is the same as the structure of the JSON geometry objects returned by the ArcGIS REST API. The use of simple syntax is not supported.
 spatial_ref  The wellknown ID of the spatial reference or a spatial
reference JSON object for the input geometries.
distance¶

arcgis.geometry.functions.
distance
(spatial_ref, geometry1, geometry2, distance_unit='', geodesic=False, gis=None)¶ The distance function is performed on a geometry service resource. It reports the 2D Euclidean or geodesic distance between the two geometries.
 Inputs:
 spatial_ref  The wellknown ID or a spatial reference JSON object for
input geometries.
 geometry1  The geometry from which the distance is to be
measured. The structure of the geometry is same as the structure of the JSON geometry objects returned by the ArcGIS REST API.
 geometry2  The geometry from which the distance is to be
measured. The structure of the geometry is same as the structure of the JSON geometry objects returned by the ArcGIS REST API.
 distanceUnit  specifies the units for measuring distance between
the geometry1 and geometry2 geometries.
 geodesic  If geodesic is set to true, then the geodesic distance
between the geometry1 and geometry2 geometries is returned. Geodesic distance is the shortest path between two points along the ellipsoid of the earth. If geodesic is set to false or not specified, the planar distance is returned. The default value is false.
find_transformation¶

arcgis.geometry.functions.
find_transformation
(in_sr, out_sr, extent_of_interest=None, num_of_results=1, gis=None)¶ The find_transformations function is performed on a geometry service resource. This function returns a list of applicable geographic transformations you should use when projecting geometries from the input spatial reference to the output spatial reference. The transformations are in JSON format and are returned in order of most applicable to least applicable. Recall that a geographic transformation is not needed when the input and output spatial references have the same underlying geographic coordinate systems. In this case, findTransformations returns an empty list. Every returned geographic transformation is a forward transformation meaning that it can be used asis to project from the input spatial reference to the output spatial reference. In the case where a predefined transformation needs to be applied in the reverse direction, it is returned as a forward composite transformation containing one transformation and a transformForward element with a value of false.
 Inputs:
 in_sr  The wellknown ID (gis,WKID) of the spatial reference or a
spatial reference JSON object for the input geometries
 out_sr  The wellknown ID (gis,WKID) of the spatial reference or a
spatial reference JSON object for the input geometries
 extent_of_interest  The bounding box of the area of interest
specified as a JSON envelope. If provided, the extent of interest is used to return the most applicable geographic transformations for the area. If a spatial reference is not included in the JSON envelope, the in_sr is used for the envelope.
 num_of_results  The number of geographic transformations to
return. The default value is 1. If num_of_results has a value of 1, all applicable transformations are returned.
from_geo_coordinate_string¶

arcgis.geometry.functions.
from_geo_coordinate_string
(spatial_ref, strings, conversion_type, conversion_mode=None, gis=None)¶ The from_geo_coordinate_string function is performed on a geometry service resource. The function converts an array of wellknown strings into xycoordinates based on the conversion type and spatial reference supplied by the user. An optional conversion mode parameter is available for some conversion types.
 Inputs:
 spatial_ref  The wellknown ID of the spatial reference or a spatial
reference json object.
 strings  An array of strings formatted as specified by
conversion_type. Syntax: [<string1>,…,<stringN>] Example: [“01N AA 66021 00000”,”11S NT 00000 62155”,
“31U BT 94071 65288”]
 conversion_type  The conversion type of the input strings.
 Valid conversion types are:
MGRS  Military Grid Reference System USNG  United States National Grid UTM  Universal Transverse Mercator GeoRef  World Geographic Reference System GARS  Global Area Reference System DMS  Degree Minute Second DDM  Degree Decimal Minute DD  Decimal Degree
 conversion_mode  Conversion options for MGRS, UTM and GARS
conversion types. Conversion options for MGRS and UTM conversion types. Valid conversion modes for MGRS are:
 mgrsDefault  Default. Uses the spheroid from the given spatial
reference.
 mgrsNewStyle  Treats all spheroids as new, like WGS 1984. The
180 degree longitude falls into Zone 60.
 mgrsOldStyle  Treats all spheroids as old, like Bessel 1841.
The 180 degree longitude falls into Zone 60.
 mgrsNewWith180InZone01  Same as mgrsNewStyle except the 180
degree longitude falls into Zone 01.
 mgrsOldWith180InZone01  Same as mgrsOldStyle except the 180
degree longitude falls into Zone 01.
 Valid conversion modes for UTM are:
utmDefault  Default. No options. utmNorthSouth  Uses north/south latitude indicators instead of
zone numbers. Nonstandard. Default is recommended
generalize¶

arcgis.geometry.functions.
generalize
(spatial_ref, geometries, max_deviation, deviation_unit, gis=None)¶ The generalize function is performed on a geometry service resource. The generalize function simplifies the input geometries using the DouglasPeucker algorithm with a specified maximum deviation distance. The output geometries will contain a subset of the original input vertices.
 Inputs:
 spatial_ref  The wellknown ID or a spatial reference JSON object for the
input geometries.
geometries  The array of geometries to be generalized. max_deviation  max_deviation sets the maximum allowable offset,
which will determine the degree of simplification. This value limits the distance the output geometry can differ from the input geometry.
 deviation_unit  A unit for maximum deviation. If a unit is not
specified, the units are derived from spatial_ref.
intersect¶

arcgis.geometry.functions.
intersect
(spatial_ref, geometries, geometry, gis=None)¶ The intersect function is performed on a geometry service resource. This function constructs the settheoretic intersection between an array of geometries and another geometry. The dimension of each resultant geometry is the minimum dimension of the input geometry in the geometries array and the other geometry specified by the geometry parameter.
 Inputs:
 spatial_ref  The wellknown ID or a spatial reference JSON object for the
input geometries.
 geometries  An array of points, multipoints, polylines, or
polygons. The structure of each geometry in the array is the same as the structure of the JSON geometry objects returned by the ArcGIS REST API.
 geometry  A single geometry of any type with a dimension equal to
or greater than the elements of geometries.
label_points¶

arcgis.geometry.functions.
label_points
(spatial_ref, polygons, gis=None)¶ The label_points function is performed on a geometry service resource. The labelPoints function calculates an interior point for each polygon specified in the input array. These interior points can be used by clients for labeling the polygons.
 Inputs:
 spatial_ref  The wellknown ID of the spatial reference or a spatial
reference JSON object for the input polygons.
 polygons  The array of polygons whose label points are to be
computed. The spatial reference of the polygons is specified by spatial_ref.
lengths¶

arcgis.geometry.functions.
lengths
(spatial_ref, polylines, length_unit, calculation_type, gis=None)¶ The lengths function is performed on a geometry service resource. This function calculates the 2D Euclidean or geodesic lengths of each polyline specified in the input array.
 Inputs:
 spatial_ref  The wellknown ID of the spatial reference or a spatial
reference JSON object for the input polylines.
 polylines  The array of polylines whose lengths are to be
computed.
 length_unit  The unit in which lengths of polylines will be
calculated. If calculation_type is planar, then length_unit can be any esriUnits constant. If calculation_type is planar and length_unit is not specified, then the units are derived from spatial_ref. If calculation_type is not planar, then length_unit must be a linear esriUnits constant such as esriSRUnit_Meter or esriSRUnit_SurveyMile. If calculation_type is not planar and length_unit is not specified, then the units are meters.
 calculation_type  calculation_type defines the length calculation
 for the geometry. The type can be one of the following values:
 planar  Planar measurements use 2D Euclidean distance to
calculate length. This type should only be used if the length needs to be calculated in the given spatial reference. Otherwise, use preserveShape.
 geodesic  Use this type if you want to calculate a length
using only the vertices of the polygon and define the lines between the vertices as geodesic segments independent of the actual shape of the polyline. A geodesic segment is the shortest path between two points on an earth ellipsoid.
 preserveShape  This type calculates the length of the geometry
on the surface of the earth ellipsoid. The shape of the geometry in its coordinate system is preserved.
offset¶

arcgis.geometry.functions.
offset
(geometries, offset_distance, offset_unit, offset_how='esriGeometryOffsetRounded', bevel_ratio=10, simplify_result=False, spatial_ref=None, gis=None)¶ The offset function is performed on a geometry service resource. This function constructs geometries that are offset from the given input geometries. If the offset parameter is positive, the constructed offset will be on the right side of the geometry. Left side offsets are constructed with negative parameters. Tracing the geometry from its first vertex to the last will give you a direction along the geometry. It is to the right and left perspective of this direction that the positive and negative parameters will dictate where the offset is constructed. In these terms, it is simple to infer where the offset of even horizontal geometries will be constructed.
 Inputs:
geometries  The array of geometries to be offset. offset_distance  Specifies the distance for constructing an offset
based on the input geometries. If the offset_distance parameter is positive, the constructed offset will be on the right side of the curve. Leftside offsets are constructed with negative values.
 offset_unit  A unit for offset distance. If a unit is not
specified, the units are derived from spatial_ref.
 offset_how  The offset_how parameter determines how outer corners
 between segments are handled. The three options are as follows:
 esriGeometryOffsetRounded  Rounds the corner between extended
offsets.
 esriGeometryOffsetBevelled  Squares off the corner after a
given ratio distance.
 esriGeometryOffsetMitered  Attempts to allow extended offsets
to naturally intersect, but if that intersection occurs too far from the corner, the corner is eventually bevelled off at a fixed distance.
 bevel_ratio  bevel_ratio is multiplied by the offset distance, and
the result determines how far a mitered offset intersection can be located before it is bevelled. When mitered is specified, bevel_ratio is ignored and 10 is used internally. When bevelled is specified, 1.1 will be used if bevel_ratio is not specified. bevel_ratio is ignored for rounded offset.
 simplify_result  if simplify_result is set to true, then self
intersecting loops will be removed from the result offset geometries. The default is false.
 spatial_ref  The wellknown ID or a spatial reference JSON object for the
input geometries.
project¶

arcgis.geometry.functions.
project
(geometries, in_sr, out_sr, transformation='', transform_forward=False, gis=None)¶ The project function is performed on a geometry service resource. This function projects an array of input geometries from the input spatial reference to the output spatial reference.
 Inputs:
geometries  The list of geometries to be projected. in_sr  The wellknown ID (gis,WKID) of the spatial reference or a
spatial reference JSON object for the input geometries.
 out_sr  The wellknown ID (gis,WKID) of the spatial reference or a
spatial reference JSON object for the input geometries.
 transformation  The WKID or a JSON object specifying the
geographic transformation (gis,also known as datum transformation) to be applied to the projected geometries. Note that a transformation is needed only if the output spatial reference contains a different geographic coordinate system than the input spatial reference.
 transform_forward  A Boolean value indicating whether or not to
transform forward. The forward or reverse direction of transformation is implied in the name of the transformation. If transformation is specified, a value for the transformForward parameter must also be specified. The default value is false.
 Example:
input_geom = [{“x”: 17568824.55, “y”: 2428377.35}, {“x”: 17568456.88, “y”: 2428431.352}] result = project(geometries = input_geom, in_sr = 3857, out_sr = 4326)
 returns:
a list of geometries in the out_sr coordinate system, for instance: [{“x”: 157.82343617279275, “y”: 21.305781607280093}, {“x”: 157.8201333369876, “y”: 21.306233559873714}]
relation¶

arcgis.geometry.functions.
relation
(geometries1, geometries2, spatial_ref, spatial_relation='esriGeometryRelationIntersection', relation_param='', gis=None)¶ The relation function is performed on a geometry service resource. This function determines the pairs of geometries from the input geometry arrays that participate in the specified spatial relation. Both arrays are assumed to be in the spatial reference specified by spatial_ref, which is a required parameter. Geometry types cannot be mixed within an array. The relations are evaluated in 2D. In other words, z coordinates are not used.
 Inputs:
 geometries1  The first array of geometries used to compute the
relations.
geometries2 The second array of geometries used to compute the relations. spatial_ref  The wellknown ID of the spatial reference or a spatial
reference JSON object for the input geometries.
 spatial_relation  The spatial relationship to be tested between the two
input geometry arrays. Values: esriGeometryRelationCross  esriGeometryRelationDisjoint  esriGeometryRelationIn  esriGeometryRelationInteriorIntersection  esriGeometryRelationIntersection  esriGeometryRelationLineCoincidence  esriGeometryRelationLineTouch  esriGeometryRelationOverlap  esriGeometryRelationPointTouch  esriGeometryRelationTouch  esriGeometryRelationWithin  esriGeometryRelationRelation
 relation_param  The Shape Comparison Language string to be
evaluated.
reshape¶

arcgis.geometry.functions.
reshape
(spatial_ref, target, reshaper, gis=None)¶ The reshape function is performed on a geometry service resource. It reshapes a polyline or polygon feature by constructing a polyline over the feature. The feature takes the shape of the reshaper polyline from the first place the reshaper intersects the feature to the last.
 Input:
 spatial_ref  The wellknown ID of the spatial reference or a spatial
reference JSON object for the input geometries.
target  The polyline or polygon to be reshaped. reshaper  The singlepart polyline that does the reshaping.
simplify¶

arcgis.geometry.functions.
simplify
(spatial_ref, geometries, gis=None)¶ The simplify function is performed on a geometry service resource. Simplify permanently alters the input geometry so that the geometry becomes topologically consistent. This resource applies the ArcGIS simplify function to each geometry in the input array.
Inputs: spatial_ref  The wellknown ID of the spatial reference or a spatial
reference JSON object for the input geometries.
geometries  The array of geometries to be simplified.
to_geo_coordinate_string¶

arcgis.geometry.functions.
to_geo_coordinate_string
(spatial_ref, coordinates, conversion_type, conversion_mode='mgrsDefault', num_of_digits=None, rounding=True, add_spaces=True, gis=None)¶ The to_geo_coordinate_string function is performed on a geometry service resource. The function converts an array of xycoordinates into wellknown strings based on the conversion type and spatial reference supplied by the user. Optional parameters are available for some conversion types. Note that if an optional parameter is not applicable for a particular conversion type, but a value is supplied for that parameter, the value will be ignored.
 Inputs:
 spatial_ref  The wellknown ID of the spatial reference or a spatial
reference json object.
 coordinates  An array of xycoordinates in JSON format to be
converted. Syntax: [[x1,y2],…[xN,yN]]
 conversion_type  The conversion type of the input strings.
 Allowed Values:
MGRS  Military Grid Reference System USNG  United States National Grid UTM  Universal Transverse Mercator GeoRef  World Geographic Reference System GARS  Global Area Reference System DMS  Degree Minute Second DDM  Degree Decimal Minute DD  Decimal Degree
 conversion_mode  Conversion options for MGRS and UTM conversion
types. Valid conversion modes for MGRS are:
 mgrsDefault  Default. Uses the spheroid from the given spatial
reference.
 mgrsNewStyle  Treats all spheroids as new, like WGS 1984. The
180 degree longitude falls into Zone 60.
 mgrsOldStyle  Treats all spheroids as old, like Bessel 1841.
The 180 degree longitude falls into Zone 60.
 mgrsNewWith180InZone01  Same as mgrsNewStyle except the 180
degree longitude falls into Zone 01.
 mgrsOldWith180InZone01  Same as mgrsOldStyle except the 180
degree longitude falls into Zone 01.
 Valid conversion modes for UTM are:
utmDefault  Default. No options. utmNorthSouth  Uses north/south latitude indicators instead of
zone numbers. Nonstandard. Default is recommended.
 num_of_digits  The number of digits to output for each of the
numerical portions in the string. The default value for num_of_digits varies depending on conversion_type.
 rounding  If true, then numeric portions of the string are
rounded to the nearest whole magnitude as specified by numOfDigits. Otherwise, numeric portions of the string are truncated. The rounding parameter applies only to conversion types MGRS, USNG and GeoRef. The default value is true.
 addSpaces  If true, then spaces are added between components of
the string. The addSpaces parameter applies only to conversion types MGRS, USNG and UTM. The default value for MGRS is false, while the default value for both USNG and UTM is true.
trim_extend¶

arcgis.geometry.functions.
trim_extend
(spatial_ref, polylines, trim_extend_to, extend_how=0, gis=None)¶ The trim_extend function is performed on a geometry service resource. This function trims or extends each polyline specified in the input array, using the userspecified guide polylines. When trimming features, the part to the left of the oriented cutting line is preserved in the output, and the other part is discarded. An empty polyline is added to the output array if the corresponding input polyline is neither cut nor extended.
 Inputs:
 spatial_ref  The wellknown ID of the spatial reference or a spatial
reference json object.
polylines  An array of polylines to be trimmed or extended. trim_extend_to  A polyline that is used as a guide for trimming or
extending input polylines.
 extend_how  A flag that is used along with the trimExtend
function. 0  By default, an extension considers both ends of a path. The
old ends remain, and new points are added to the extended ends. The new points have attributes that are extrapolated from adjacent existing segments.
 1  If an extension is performed at an end, relocate the end
point to the new position instead of leaving the old point and adding a new point at the new position.
 2  If an extension is performed at an end, do not extrapolate
the endsegment’s attributes for the new point. Instead, make its attributes the same as the current end. Incompatible with esriNoAttributes.
 4  If an extension is performed at an end, do not extrapolate
the endsegment’s attributes for the new point. Instead, make its attributes empty. Incompatible with esriKeepAttributes.
8  Do not extend the ‘from’ end of any path. 16  Do not extend the ‘to’ end of any path.
union¶

arcgis.geometry.functions.
union
(spatial_ref, geometries, gis=None)¶ The union function is performed on a geometry service resource. This function constructs the settheoretic union of the geometries in the input array. All inputs must be of the same type.
Inputs: spatial_ref  The wellknown ID of the spatial reference or a spatial
reference json object.
geometries  The array of geometries to be unioned.